Power Rule.
Sum and Difference Rule.
The derivative of exponential and logarithmic functions
The Chain Rule
The Product Rule
The Quotient Rule
The derivative of trigonometric functions
How do I find the derivative of a function defined algebraically without using the limit definition of the derivative?
How do I find the derivative of a combination of two or more functions if the functions are defined graphically, or by a table of values
Chapter 4: Applications of the derivative.
Graph Theory- local extrema, absolute extrema, concavity and points of inflection.
Particle motion along a line - position, velocity and acceleration.
Optimization.
Where and what are the local or absolute extreme
values of a function ?
Where are the points of inflection of a function?
What is the relationship between the position, velocity and acceleration of an object moving along a line?
How do I calculated the distance a particle has traveled along a line, given that it changes direction ?
How do I interpret and calculate maximum and minimum values of a function which represents a physical quantity in a variety of practical situations?
Determine local and absolute extreme values, and points of inflection of a function defined algebraically.
Determine velocity and acceleration and distance traveled by a particle along a line when its position function is given.
Determine maximum and minimum volumes and surface areas of geometric figures under given constraints.
Solve minimal path problems.
Applied Calculus ; 3rd Edition. Hughes-Hallett/Gleason/Lock/Flath et al
Calculus: Concepts and Calculators. George Best
AP Calculus Problems
How do we measure distance traveled from a velocity-time graph?
How is total change in a function calculated from the rate of change of a function?
What is the relationship between the definite integral and the area under a curve?
How is the area between curves calculated?
Estimate the area under a curve using Riemann sums.
Understand that the limit of a Riemann sum leads to the definite integral of a function.
Calculate the total change of a function from its rate of change function.
Interpret the definite integral of a function in real-world problems, using correct units.
Determine the area between functions.
Applied Calculus: 3rd Edition. Hughes-Hallett/Gleason/Lock/Flath et al.
Calculus: Graphical, Numerical, Algebraic: Finney/Demana/Waits/Kennedy.
Z:\Faculty\Gentry\gentry\DOCS\Calculus\definite_integral.tii
Calculus in Motion. Audrey S. Weeks
Quiz
Test
Weeks 14-15
The Antiderivative and the Fundamental Theorem of Calculus
What is an anti-derivative?
What are the properties of anti-derivatives?
How do we find the anti-derivative of a function?
How is the connection between a definite integral and the anti-derivative of a function?
How can we sketch the graph of the anti-derivative of a function defined graphically?
What is the Fundamental Theorem of Calculus?
Construct anti-derivatives analytically.
Use the properties of anti-derivatives.
Integration by substitution.
Use the Fundamental Theorem to compute definite integrals.
Construct the graph of a function, given the graph of its derivative.
Use the fundamental theorem to compute areas between graphs.
How can the limit of a Riemann Sum or a definite integral be used to calculate the volume of a solid?
Approximate the volume of a solid of revolution using the sum of infinitesimally small cylinders.
Use a definite integral to find the volume of a solid of revolution.
Use a definite integral to find the volume of a solid of constant cross-section.
Calculus :Graphical, Numerical,Algebraic. Finney/Demana/Waits/Kennedy.
Calculus:Concepts and Applications. Paul A. Foerster
Calculus in Motion. Audrey S. Weeks
1 -2
What is the derivative of a function and what does it tell us about the function?
How do I estimate f'(a) if function f is defined graphically, algebraically or by a table of values?
How do I sketch the derivative of a function defined graphically ?
What is the second derivative of a function and what does it tell us about the behavior of the function?
What is the formal definition of the derivative ?
Estimation of derivatives from a graph, table of values or a formula.
Calculation and estimation of the second derivative to determine the concavity of a function.
Understand the relation between the sign of f' and whether f is increasing or decreasing.
Sketch the graph of f' from the graph of f.
Finding f'(x) using the limit definition of the derivative
Calculus in Motion software by Audrey Weeks.
The derivative Plotter
http://www.joma.org/images/upload_library/4/vol4/kaskosz/derapp.html
Power Rule.
Sum and Difference Rule.
The derivative of exponential and logarithmic functions
The Chain Rule
The Product Rule
The Quotient Rule
The derivative of trigonometric functions
How do I find the derivative of a combination of two or more functions if the functions are defined graphically, or by a table of values
Derivative Bingo
http://www.quia.com/cb/37133.html
Graph Theory- local extrema, absolute extrema, concavity and points of inflection.
Particle motion along a line - position, velocity and acceleration.
Optimization.
values of a function ?
Where are the points of inflection of a function?
What is the relationship between the position, velocity and acceleration of an object moving along a line?
How do I calculated the distance a particle has traveled along a line, given that it changes direction ?
How do I interpret and calculate maximum and minimum values of a function which represents a physical quantity in a variety of practical situations?
Determine velocity and acceleration and distance traveled by a particle along a line when its position function is given.
Determine maximum and minimum volumes and surface areas of geometric figures under given constraints.
Solve minimal path problems.
Calculus: Concepts and Calculators. George Best
AP Calculus Problems
How is total change in a function calculated from the rate of change of a function?
What is the relationship between the definite integral and the area under a curve?
How is the area between curves calculated?
Understand that the limit of a Riemann sum leads to the definite integral of a function.
Calculate the total change of a function from its rate of change function.
Interpret the definite integral of a function in real-world problems, using correct units.
Determine the area between functions.
Calculus: Graphical, Numerical, Algebraic: Finney/Demana/Waits/Kennedy.
Z:\Faculty\Gentry\gentry\DOCS\Calculus\definite_integral.tii
Calculus in Motion. Audrey S. Weeks
Test
What are the properties of anti-derivatives?
How do we find the anti-derivative of a function?
How is the connection between a definite integral and the anti-derivative of a function?
How can we sketch the graph of the anti-derivative of a function defined graphically?
What is the Fundamental Theorem of Calculus?
Use the properties of anti-derivatives.
Integration by substitution.
Use the Fundamental Theorem to compute definite integrals.
Construct the graph of a function, given the graph of its derivative.
Use the fundamental theorem to compute areas between graphs.
Antiderivative Bingo.
Test
Use a definite integral to find the volume of a solid of revolution.
Use a definite integral to find the volume of a solid of constant cross-section.
Calculus:Concepts and Applications. Paul A. Foerster
Calculus in Motion. Audrey S. Weeks
Test